Final answer:
In Yugoslavia, Eastern Orthodox Christianity, Roman Catholicism, and Islam played prominent roles in its ethnic divisions and subsequent dissolution. Judaism, while present, did not have a prominent role in the country's breakdown.
Step-by-step explanation:
The religious landscape in Yugoslavia before its dissolution was predominantly comprised of Eastern Orthodox Christianity, Roman Catholicism, and Islam.
The prominent religions corresponding to the ethnic groups were Eastern Orthodox Christianity for the Serbs, Montenegrins, and Macedonians, Roman Catholicism for the Slovenes and Croats, and Islam for the Bosniaks.
Considering the historical context, the religions that played a prominent role in Yugoslavia were Eastern Orthodox Christianity, Roman Catholicism, and Islam.
While Jewish communities did exist in Yugoslavia, historically faced limitations and increased opposition post-Rome, they did not play a prominently defining role in the ethnic and political divides that led to the breakdown of Yugoslavia in the 1990s.
Thus, the religion that did not play a prominent role in Yugoslavia, particularly in the context of the dissolution of the country, was Judaism.